Remark 2.4 
By [[1]}, Theorem 2.14] and [[2]}, Theorem 5.5], if a Deligne-Mumford \(S\) -stack \(\mathcal {X}\)  has a projective coarse moduli scheme, then \(\mathcal {X}\)  is global quotient stack over \(S\)  if and only if \(\mathcal {X}\)  possesses a generating sheaf.

